Hi,

Could you please help me solve? Please do not use ChatGPT or any other type of AI :)

1/3 [10 pts] Unsteady mass conservation (after Smits) A fluid flows through a two-dimensional duct of width, W, as shown in Figure 1. At the entrance to the box (face 1), the flow is one-dimensional and the fluid has density p; and velocity U;. At the exit (face 2), the fluid has a uniform density, p2 but the velocity varies across the duct as shown. You are asked to find the rate at which the average density inside the box is changing with time. (a) [2 pts] Sketch a suitable control volume for this problem. (b) [2 pts] Define an average density within the control volume. (b) [6 pts] Find an expression for the time rate of change of this average density